In a printer having a duplex loop, the duplex sheets on which one page has been printed on one side thereof are continuously passed through the duplex loop in which they are reversed and recirculated to the printing station so that the second page can be printed on the second side. This has the advantage that no intermediate tray is necessary for accommodating the half-completed duplex sheets between the first and second print cycle, so that no limitations as to the capacity of the intermediate tray need to be observed, and the first completed duplex copies are available in the output tray only a short time after the printing operation has started. The duplex loop has a predetermined capacity dependent on the length of the duplex loop and on the size of the sheets.
For example N-sheets of equal size can be present in the duplex loop. The duplex loop may also contain sheets of different sizes. This does not affect the general applicability of the method described herein.
The operation of the printing station in which one complete page is printed on one side of a sheet will be termed "print cycle" hereinafter. The sequence in which the various pages of a document are printed in the printing station must fulfill the condition that there always exists a predetermined distance, dependent on the size of the sheet, between the printing of the first page and the second page on the same sheet. For example, if the capacity of the duplex loop is 5 sheets and a document consists of ten pages to be printed on five duplex sheets, then the second, fourth, sixth, eighth and tenth page may sequentially be printed on the respective first sides of the sheets, and afterwards the first, third, fifth, seventh and ninth page are sequentially printed on the respective second side of each sheet, so that one copy of the whole document can be completed within ten cycles. If the copies are deposited "face down" in the output tray, then a collated set of copies will be obtained, i.e., the order of pages in the stack of copy sheets will be the same as in the original document.
However, if the document has only nine pages, then the fifth sheet would be a simplex sheet which needs not be circulated through the duplex loop. Then, the printing sequence would be 2-4-6-8-skip-1-3-5-7-9. The "skip" in the fifth print cycle is necessary in order to make sure that pages 1 and 2 are printed on the same sheet. Such skips in the printing sequence mean that the printing station is inoperative during certain cycles. This leads to a loss of productivity of the printer, in particular when the above sequence is repeated several times in order to print multiple copies of the document.
Several approaches have been made to increase the productivity of this type of printer by scheduling the sequence of pages such that the number of skips is reduced.
U.S. Pat. No. 5,095,342 discloses a scheduling method according to the preamble of claim 1 which may involve a plurality of print jobs, so that the skips occurring at the end of one job can be filled with the first pages of a subsequent job, of course without changing the order in which the copies are completed. This method also involves the transformation of simplex sheets into duplex sheets, which means that a sheet is treated as a duplex sheet and is circulated through the duplex loop, although one side of this sheet remains empty. In conjunction with the scheduling algorithm disclosed in this document, such transformation of simplex sheets into duplex sheets may under certain conditions lead to a further enhancement of productivity. However, whether these conditions are fulfilled or not can only be determined when the page structure (simplex or duplex) is known beforehand for the totality of jobs involved. As an additional measure for eliminating skips, it is proposed in this document to advance the scheduling of some duplex pages ahead of the last simplex page at a simplex-to-duplex transition, thereby to avoid skips without changing the output order of the sheets.
U.S. Pat. No. 4,453,841 discloses a scheduling method in which the scheduled sequence consists of a predefined string which is then cyclically repeated in accordance with the number of copies to be made. One of a plurality of predefined strings is selected dependent on the number of pages of the job. Thus, this scheduling process also requires that the total number of pages to be printed is known beforehand.
U.S. Pat. No. 4,918,490 discloses a method in which the jobs to be printed are divided into a number of batches, each batch consisting of 2N pages when N is the capacity of the duplex loop. Each batch is sequenced in the manner described in the opening paragraphs of the present description. Depending on the number of pages per job, there may still remain a considerable number of skips which lead to production losses when the number of copies to be made is large. According to another method discussed in the same document, the pages are sequenced such that skips will occur only during the first N cycles and the last N cycles of the sequence but not in the middle part thereof. This method also has a comparatively low efficiency when the number of pages per job is small and a large number of copies has to be made.